Malaysian Prime Minister Najib Razak has so far weathered calls for him to quit over a funding scandal, but as his party opens its annual meeting on Tuesday he must address how it can dodge a defeat at the next election that would end its 58-year rule.

Malaysia's anti-corruption agency has questioned Najib over deposits of nearly $700 million funds made to his personal bank account, while state fund 1Malaysia Development Berhad (1MDB) is facing probes in several countries over allegations of graft. The scandals have shaken investors in Southeast Asia's third-biggest economy and rocked public confidence in the coalition led by Najib's United Malays National Organization (UMNO), which has held power since independence in 1957.

"In Malaysia, if you control UMNO you control the country," said Ooi Kee Beng, deputy director at the Singapore-based ISEAS-Yusof Ishak Institute. "The only way UMNO can turn things around for itself is with a new leader, a new agenda and a new direction in leadership."

Backing for the government among the ethnic Malay majority that forms the bedrock of UMNO's support sank to 31 percent in October, from 52 percent in January, according to the most recent poll from research firm Merdeka Center.

UMNO suffered its worst ever election result in 2013, when the ruling coalition clung on to a parliamentary majority despite losing the popular vote as it was deserted by ethnic Chinese voters and many urban dwellers.

Ahead of the party's annual general assembly, Najib appealed for unity.

"Stop the bickering, stop spreading and believing slander, and stop doing things that don't bring any benefit," Najib said in his Facebook post on Friday.

Najib, 62, still enjoys the backing of most of UMNO's powerful division chiefs, and even his fiercest internal critics accept that he cannot be unseated.

The opposition is also weak without charismatic leader Anwar Ibrahim, who was jailed on charges of sodomy in February, a verdict his supporters say was politically motivated.

PM under pressure

But pressure is nonetheless mounting on Najib over a scandal that erupted in July, when the Wall Street Journal reported that investigators looking into 1MDB found nearly $700 million was transferred to the prime minister's own bank accounts.

The uncertainty created has hit an economy already reeling from falling oil and gas prices, with the ringgit currency losing nearly a quarter of its value against the dollar this year.

Najib, who chairs 1MDB's advisory board, has denied taking any funds for personal gain and Malaysia's anti-graft agency, MACC, has said the money was a political donation from a Middle Eastern donor.

But foreign agencies, including the FBI, are investigating 1MDB. MACC took a statement from Najib on Saturday.

A handful of UMNO division chiefs called last month for Najib's resignation and the party's second-in-command, Muhyiddin Yassin, has demanded a fuller explanation on the 1MDB issue.

Najib's biggest threat, however, comes from influential former Prime Minister Mahathir Mohamad, who has said UMNO will lose the next election in 2018 if Najib remains in charge.

Najib's supporters acknowledge UMNO is facing a crisis.

"We are far from perfect, we have weaknesses and as we grow, mistakes are inevitable," UMNO vice president and Malaysia's Defense Minister Hishammuddin Hussein was quoted saying by the state news agency Bernama, adding UMNO faced a "test of trust".

Najib has reacted to the growing opposition by cracking down on dissent. A new National Security Council Bill was pushed through parliament last week, which opponents say gives the government sweeping powers that threaten human rights.

In a break from tradition, the party's deputy president, Muhyiddin, will not speak at the assembly. He was sacked as deputy prime minister in July for speaking against Najib. Media access will also be tightly controlled.

In his latest blog post former leader Mahathir described this year's meeting as futile.

"Proceedings will be closed-door. And only the president's speech will be aired," he said.